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THE UNIVERSITY OF CHICAGO 

FOUNDED BY JOHN D. ROCKEFELLER 



THE NATURE OF HYPOTHESIS 



A DISSERTATION 

SUBMITTED TO THE FACULTY OF THE GRADUATE SCHOOL OF ARTS AND 

LITERATURE IN CANDIDACY FOR THE DEGREE OF 

DOCTOR OF PHILOSOPHY 

(department of philosophy) 



BY 

MYRON LUCIUS ASHLEY 



CHICAGO 
1903 






[The chapter constituting this Dissertation is taken from a larger volume 
entitled Studies in Logical Theory, which has appeared as "Volume XI, Second 
Series, of the Decennial Publications of the University of Chicago.] 



lAy-*~vAT 



[For the pages on*Mill and Whewell 
the author wishes to acknowledge his 
indebtedness to Professor Dewey.] 



PRINTED AT THE UNIVERSITY OF CHICAGO PRESS 



VII 

THE NATURE OF HYPOTHESIS 

In the various discussions of the hypothesis which have 
appeared in works on inductive logic and in writings on 
scientific method, its structure and function have received 
considerable attention, while its origin has been compara- 
tively neglected. The hypothesis has generally been treated 
as that part of scientific procedure which marks the stage 
where a definite plan or method is proposed for dealing with 
new or unexplained facts. It is regarded as an invention 
for the purpose of explaining the given, as a definite con- 
jecture which is to be tested by an appeal to experience to 
see whether deductions made in accordance with it will be 
found true in fact. The function of the hypothesis is to 
unify, to furnish a method of dealing with things, and its 
structure must be suitable to this end. It must be so 
formed that it will be likely to prove valid, and writers 
have formulated various rules to be followed in the forma- 
tion of hypotheses. These rules state the main require- 
ments of a good hypothesis, and are intended to aid in a 
general way by pointing out certain limits within which it 
must fall. 

In respect to the origin of the hypothesis, writers have 
usually contented themselves with pointing out the kind of 
situations in which hypotheses are likely to appear. But 
after this has been done, after favorable external conditions 
have been given, the rest must be left to "genius," for 
hypotheses arise as "happy guesses," for which no rule or 
law can be given. In fact, the genius differs from the 
ordinary plodding mortal in just this ability to form fruitful 

143 



144: Studies in Logical Theory 

hypotheses in the midst of the same facts which to other less 
gifted individuals remain only so many disconnected expe- 
riences. 

This unequal stress which has been laid on the structure 
and function of the hypothesis in comparison with its origin 
may be attributed to three reasons: (1) The facts, or data, 
which constitute the working material of hypotheses are 
regarded as given to all alike, and all alike are more or less 
interested in systematizing and unifying experience. The 
purpose of the hypothesis and the opportunity for forming it 
are thus practically the same for all, and hence certain defi- 
nite rules can be laid down which will apply to all cases 
where hypotheses are to be employed. (2) But beyond this 
there seems to be no clue that can be formulated. There is 
apparently a more or less open acceptance of the final answer 
of the boy Zerah Colburn, who, when pressed to give an 
explanation of his method of instantaneous calculation, ex- 
claimed in despair: "Grod put it into my head, and I can't 
put it into yours." 1 (3) And, furthermore, there is very often 
a strong tendency to disregard investigation into the origin 
of that which is taken as given, for, since it is already 
present, its origin, whatever it may have been, can have 
nothing to do with what it is now. The facts, the data, 
are here, and must be dealt with as they are. Their past, 
their history or development, is entirely irrelevant. So, 
even if we could trace the hypothesis farther back on the 
psychological side, the investigation would be useless, for 
the rules to which a good hypothesis must conform would 
remain the same. 

Whether or not it can be shown that Zerah Colburn's 
ultimate explanation is needed in logic as little as Laplace 
asserted a similar one to 'be required in his celestial me- 

i De Morgan, Budget of Paradoxes, pp. 55, 56 ; quoted by Welton, Logic, Vol. 
H, p. 60. 



The Nature of Hypothesis 145 

chanics, it may at least be possible to defer it to some extent 
by means of a further psychological inquiry. It will be 
found that psychological inquiry into the origin of the 
hypothesis is not irrelevant in respect to an understanding 
of its structure and function; for origin and function can- 
not be understood apart from each other, and, since struc- 
ture must be adapted to function, it cannot be independent 
of origin. In fact, origin, structure, and function are organ- 
ically connected, and each loses its meaning when absolutely 
separated from each other. It will be found, moreover, that 
the data which are commonly taken as the given material 
are not something to which the hypothesis is subsequently 
applied, but that, instead of this external relation between 
data and hypothesis, the hypothesis exercises a directive func- 
tion in determining what are the data. In a word, the main 
object of this discussion will be to contend against making 
a merely convenient and special way of regarding the 
hypothesis a full and adequate one. Though we speak of 
facts and of hypotheses that may be applied to them, it 
must not be forgotten that there are no facts which remain 
the same whatever hypothesis be applied to them ; and that 
there are no hypotheses which are hypotheses at all except 
in reference to their function in dealing with our subject- 
matter in such a way as to facilitate its factual apprehension. 
Data are selected in order to be determined, and hypotheses 
are the ways in which this determination is carried on. If, 
as we shall attempt to show, the relation between data and 
hypothesis is not external, but strictly correlative, it is evi- 
dent that this fact must be taken into account in questions 
concerning deduction and induction, analytic and synthetic 
judgments, and the criterion of truth. Its bearing must be 
recognized in the investigation of metaphysical problems as 
well, for reality cannot be independent of the knowing 
process. In a word, the purpose of this discussion of the 



146 Studies in Logical Theory 

hypothesis is to determine its nature a little more precisely 
through an investigation of its rather obscure origin, and to 
call attention to certain features of its function which have 
not generally been accorded their due significance. 



TTie hypothesis as predicate. — It is generally admitted 
that the function of the hypothesis is to provide a way of 
dealing with the data or subject-matter which we need to 
organize. In this use of the hypothesis it appears in the 
r6le of predicate in a judgment of which the data, or facts, 
to be construed constitute the subject. 

In his attempts to reduce the movements of the planets 
about the sun to some general formula, Kepler finally hit 
upon the law since known as Kepler's law, viz., that the 
squares of the periodic times of the several planets are pro- 
portional to the cubes of their mean distances from the sun. 
This law was first tentatively advanced as a hypothesis. 
Kepler was not certain of its truth till it had proved its 
claim to acceptance. Neither did Newton have at first any 
great degree of assurance in regard to his law of gravitation, 
and was ready to give it up when he failed in his first attempt 
to test it by observation of the moon. And the same thing 
may be said about the caution of Darwin and other investi- 
gators in regard to accepting hypotheses. The only reason 
for their extreme care in not accepting at once their tentative 
formulations or suggestions was the fear that some other 
explanation might be the correct one. This rejection of 
other possibilities is the negative side of the matter. TTe 
become confident that our hypothesis is the right one as we 
lose confidence in other possible explanations ; and it might 
be added, without falling into a circle, that we lose confidence 
in the other possibilities as we become more convinced of 
our hypothesis. 



The Nature of Hypothesis 147 

It appears that such may be the relation of the positive 
and negative sides in case of such elaborate hypotheses as 
those of Kepler and Newton; but is it true where our 
hypotheses are more simple? It is not easy to understand 
why the fact that the hypothesis is more simple, and the 
time required for its formulation and test a good deal 
shorter, should materially change the state of affairs. The 
question remains: Why, if there is no opposition, should 
there be any uncertainty ? In all instances, then, the hypothe- 
sis appears as one among other possible predicates which 
may be applied to our data taken as subject-matter of a 
judgment. 

The predicate as hypothesis. — Suppose, then, the 
hypothesis is a predicate; is the predicate necessarily a 
hypothesis? This is the next question we are called upon 
to answer, and, since the predicate cannot very well be taken 
aside from the judgment, our question involves the nature 
of the judgment. 

While it will not be necessary to give a very complete 
account of the various definitions of the judgment that might 
be adduced, still the mention of a few of the more prominent 
ones may serve to indicate that something further is needed. 
In definitions of the judgment sometimes the subjective side 
is emphasized, sometimes the objective side, and in other 
instances there are attempts to combine the two. For 
instance, Lotze regards the judgment as the idea of a unity 
or relation between two concepts, with the further implica- 
tion that this connection holds true of the object referred 
to. J. S. Mill says that every proposition either affirms or 
denies existence, coexistence, sequence, causation, or resem- 
blance. Trendelenburg regards the judgment as a form of 
thought which corresponds to the real connection of things, 
while Ueberweg states the case a little differently, and says 
that the essence of judgment consists in recognizing the 



148 Studies in Logical Theory 

objective validity of a subjective connection of ideas. Royce 
points to a process of imitation and holds that in the judg- 
ment we try to portray by means of the ideas that enter into 
it. Ideas are imitative in their nature. Sigwart's view of 
the judgment is that in it we say something about some- 
thing. With him the judgment is a synthetic process, while 
Wundt considers its nature analytic and holds that, instead 
of uniting, or combining, concepts into a whole, it separates 
them out of a total idea or presentation. Instead of blend- 
ing parts into a whole, it separates the whole into its con- 
stituent parts. Bradley and Bosanquet both hold that in 
the judgment an ideal content comes into relation with 
reality. Bradley says that in every judgment reality is 
qualified by an idea, which is symbolic. The ideal content 
is recognized as such, and is referred to a reality beyond the 
act. This is the essence of judgment. Bosanquet seems 
to perceive a closer relation between idea and reality, for 
although he says that judgment is the "intellectual function 
which defines reality by significant ideas," he also tells us 
that "the subject is both in and out of the judgment, as 
Reality is both in and out of my consciousness." 

In all these definitions of judgment the predicate appears 
as ideal. An ideal content is predicated of something, 
whether we regard this something as an idea or as reality 
beyond, or as reality partly within and partly without the 
act of judging ; and it is ideal whether we consider it as one 
of the three parts into which judgments are usually divided, 
or whether we say, with Bosanquet and Bradley, that sub- 
ject, predicate, and copula all taken together form a single 
ideal content, which is somehow applied to reality. More- 
over, we not only judge about reality, but it seems to be 
quite immaterial to reality whether we judge concerning it 
or not. 

Many of our judgments prove false. Not only do we err 



The Nature of Hypothesis 149 

in our judgments, but we often hesitate in making them for 
fear of being wrong; we feel there are other possibilities, 
and our predication becomes tentative. Here we have some- 
thing very like the hypothesis, for our ideal content shows 
itself to be a tentative attempt in the presence of alterna- 
tives to qualify and systematize reality. It appears, then, 
on the basis of the views of the judgment that have been 
mentioned, that not only do we find the hypothesis taking 
its place as the predicate of a judgment, but the predicate is 
itself essentially of the nature of a hypothesis. 

In the views of the judgment so far brought out, reality, 
with which it is generally admitted that the judgment 
attempts to deal in some way, appears to lie outside the act 
of judging. Now, everyone would say that we make some 
advance in judging, and that we have a better grasp of 
things after than before. But how is this possible if reality 
lies without or beyond our act of judging? Is the reality 
we now have the same that we had to begin with ? If so, 
then we have made no advance as far as the real itself is 
concerned. If merely our conception of it has changed, 
then it is not clear why we may not be even worse off than 
before. If reality does lie beyond our judgment, then how, 
in the nature of the case, can we ever know whether we 
have approached it or have gone still farther away? To 
make any claim of approximation implies that we do reach 
reality in some measure, at least, and, if so, it is difficult to 
understand how it lies beyond, and is independent of, the 
act of judging. 

Further analysis of judgment. — It remains to be seen 
whether a further investigation of the judgment will still 
show the predicate to be a hypothesis. It is evident that in 
some cases the judgment appears at the end of a more or 
less pronounced reflective process, during which other pos- 
sible judgments have suggested themselves, but have been 



150 Studies in Logical Theory 

rejected. The history of scientific discovery is filled with 
cases which illustrate , the nature of the process by which a 
new theory is developed. For instance, in Darwin's Forma- 
tion of Vegetable Mould through the Action of Earth Worms, 
we find the record of successive steps in the development of 
his hypothesis. Darwin suspected from his observations that 
vegetable mold was due to some agency which was not yet 
determined. He reasoned that if vegetable mold is the result 
of the life-habits of earthworms, i. e., if earth is brought up 
by them from beneath the surface and afterward spread out 
by wind and rain, then small objects lying on the surface of the 
ground would tend to disappear gradually below the surface. 
Facts seemed to support his theory, for layers of red sand, 
pieces of chalk, and stones were found to have disappeared 
below the surface in a greater or less degree. A common 
explanation had been that heavy objects tend to sink in soft 
soil through their own weight, but the earthworm hypothe- 
sis led to a more careful examination of the data. It was 
found that the weight of the object and the softness of the 
ground made no marked difference, for sand and light objects 
sank, and the ground was not always soft. In general, it 
was shown that where earthworms were found vegetable 
mold was also present, and vice versa. 

In this investigation of Darwin's the conflicting explana- 
tions of sinking stones appear within the main question of 
the formation of vegetable mold by earthworms. The facts 
that disagreed with the old theory about sinking stones were 
approached through this new one. But the theories had some- 
thing in common, viz., the disappearance of the stones or 
other objects : they differed in their further determination of 
this disappearance. In this case it may seem as if the facts 
which were opposed to the current theory of sinking stones 
were seen to be discrepant only after the earthworm hypothe- 
sis had been advanced ; the conflict between the new facts 



The Nature of Hypothesis 151 

and the old theory appears to have arisen through the influ- 
ence of the new theory. 

There are cases, however, where the facts seem clearly to 
contradict the old theory and thus give rise to a new one. 
For example, we find in Darwin's introduction to his Origin 
of Species the following: "In considering the origin of 
species it is quite conceivable that a naturalist reflecting on 
the mental affinities of organic beings, on their embryologi- 
cal relations, their geographical distribution, geological suc- 
cession, and other such facts, might come to the conclusion 
that species had not been independently created but had 
descended, like varieties, from other species." It would 
seem from this statement that certain data were found for 
which the older theory of independent creation did not offer 
an adequate explanation. And yet the naturalist would 
hardly " reflect" on all these topics in a comparative way 
unless some other mode of interpretation were already dawn- 
ing upon him, which led him to review the accepted reflec- 
tions or views. 

As a more simple illustration, we may cite the common 
experience of a person who is uncertain concerning the 
identity of an approaching object, say, another person. At 
first he may not be sure it is a person at all. He then sees 
that it is someone, and as the person approaches he is inclined 
to believe him to be an acquaintance. As the supposed 
acquaintance continues to approach, the observer may dis- 
tinguish certain features that cause him to doubt, and then 
relinquish his supposition that it is an acquaintance. Or, 
he may conclude at once that the approaching person is 
another individual he knows, and the transition may be so 
readily made from one to the other that it would be difficult 
to determine whether the discordant features are discordant 
before the new supposition arises, or whether they are not 
recognized as conflicting till this second person is in mind. 



152 Studies in Logical Theory 

Or, again, the identification of the new individual and the 
discovery of the features that are in conflict with the first 
supposition may appear to go on together. 

Now, marked lines of likeness appear between this 
relatively simple judgment and the far more involved ones 
of scientific research. In the more extended scientific 
process we find data contradicting an old theory and a new 
hypothesis arising to account for them. The hypothesis is 
tested, and along with its verification we have the rejection, 
or rather the modification, of the old theory. Similarly, in 
case of the approaching stranger all these features are 
present, though in less pronounced degree. In scientific 
investigation there is an interval of testing by means of more 
careful consideration of the data and even actual experimen- 
tation. Before an explanation is accepted subject to test, a 
number of others may have been suggested and rejected. 
They may not have received even explicit recognition. In 
case of the identification of the stranger this feature is 
also present. Between two fairly definite attempts to 
identify the mind does not remain a mere blank or station- 
ary, but other possible identifications may be suggested 
which do not have sufficient plausibility to command serious 
attention; they are only comparatively brief suggestions or 
tendencies. 

It is to be noted that in all these instances the first sup- 
position was not entirely abandoned, but was modified and 
more exactly determined. (Why it could not be wholly 
false and the new one wholly new, will be considered later 
in connection with discussion of the persistence and re- 
formation of habit.) There was such a modification of the 
old theory as would meet the requirements of the new data, 
and the new explanations thus contained both old and new 
features. 

We have seen that the predicate of the scientific judg- 



The Nature of Hypothesis 153 

ment is a hypothesis which is consciously applied to certain 
data. If the similarity between the scientific judgment and 
the more immediate and simple judgment is to be main- 
tained, it is clear that the predicate of the simple judgment 
must be of like nature. The structure of the two varieties 
of judgment differs only in the degree of explicitness which 
the hypothesis acquires. That is, the predicate of a judg- 
ment, as such, is ideal; it is meaning, significant quality. 
If conditions are such as to make the one judging hesitant 
or doubtful the mind wavers; the predicate is not applied 
at once to the determination or qualification of data, and 
hence comes to more distinct consciousness on its own 
account. From being "ideal," it becomes an idea. Yet its 
sole purpose and value remains in its possible use to inter- 
pret data. Let the idea remain detached, and let the query 
whether it be a true predicate (i. e., really fit to be employed 
in determining the present data) become more critical, and 
the idea becomes clearly a hypothesis. 1 In other words, the 
hypothesis is just the predicate-function of judgment defi- 
nitely apprehended and regarded with reference to its nature 
and adequacy. 

Psychological analysis of judgment. — This hypothetical 
nature of the predicate will be even more apparent after a 
further psychological analysis, which, while applying more 
directly to the simpler and more immediate judgments, may 
be extended to the more involved ones as well. 

In psychological terms, we may say, in explanation of 
the judging process, that some stimulus to action has failed 
to function properly as a stimulus, and that the activity 

lAdvanced grammarians treat this matter in a way which should be instructive 
to logicians. The hypothesis, says Sweet (§ 295 of A New English Grammar, Logical 
and Historical, Oxford, 1892), suggests an affirmation or negation "as objects of 
thought. 1 ' " In fact, we often say supposing (that is, ' thinking ') it is true, instead 
of if it is true.^ In a word, the hypothetical judgment as such puts explicitly before 
us the content of thought, of the predicate or hypothesis ; and in so far is a moment 
in judgment rather than adequate judgment itself. 



15-t Studies in Logical Theory 

which was going on has thus been interrupted. Response 
in the accustomed way has failed. In such a case there 
arises a division in experience into sensation content as sub- 
ject and ideal content as predicate. In other words, an 
activity has been going on in accordance with established 
habits, but upon failure of the accustomed stimulus to be 
longer an adequate stimulus this particular activity ceases, 
and is resumed in an integral form only when a new habit 
is set up to which the new or altered stimulus is adequate. It 
is in this process of reconstruction that subject and predicate 
appear. Sensory quality marks the point of stress, or 
seeming arrest, while the ideal or imaged aspect defines the 
continuing activity as projected, and hence that with which 
start is to be made in coping with the obstacle. It serves as 
standpoint of regard and mode of indicated behavior. The 
sensation stands for the interrupted habit, while the image 
stands for the new habit, that is, the new way of dealing 
with the subject-matter. 1 

It appears, then, that the purpose of the judgment is to 
obtain an adequate stimulus in that, when stimulus and 
response are adjusted to each other, activity will be resumed. 
But if this reconstruction and response were to follow at 
once, would there be any clearly defined act of judging at 
all? In such a case there would be no judgment, properly 
speaking, and no occasion for it. There would be simply a 
ready transition from one line of activity to another; we 
should have changed our method of reaction easily and 
readily to meet the new requirements. On the one hand, 
our subject-matter would not have become a clearly recog- 
nized datum with which we must deal; on the other hand, 
there would be no ideal method of construing it. 2 Activity 

i This carries with it, of course, the notion that " sensation " and " image " are 
not distinct psychical existences in themselves, but are distinguished logical forces. 

2 Concerning the strict correlativity of subject and predicate, data and hypo- 
thesis, see pp. 182.1S3. 



The Nature of Hypothesis 155 

would have changed without interruption, and neither sub- 
ject nor predicate would have arisen. 

In order that judgment may take place there must be 
interruption and suspense. Under what conditions, then, is 
this suspense and uncertainty possible ? Our reply must be 
that we hesitate because of more or less sharply defined 
alternatives ; we are not sure which predicate, which method 
of reaction, is the right one. The clearness with which 
these alternatives come to mind depends upon the degree of 
explicitness of the judgment, or, more exactly, the explicit- 
ness of the judgment depends upon the sharpness of these 
alternatives. Alternatives may be carefully weighed one 
against the other, as in deliberative judgments ; or they may 
be scarcely recognized as alternatives, as in the case in the 
greater portion of our more simple judgments of daily con- 
duct. 

The predicate is essentially hypothetical. — If we review 
in a brief resume" the types of judgment we have considered, 
we find in the explicit scientific judgment a fairly well- 
defined subject-matter which we seek further to determine. 
Different suggestions present themselves with varying 
degrees of plausibility. Some are passed by as soon as 
they arise. Others gain a temporary recognition. Some 
are explicitly tested with resulting acceptance or rejec- 
tion. The acceptance of any one explanation involves the 
rejection of some other explanation. During the process of 
verification or test the newly advanced supposition is recog- 
nized to be more or less doubtful. Besides the hypothesis 
which is tentatively applied there is recognized the possi- 
bility of others. In the disjunctive judgment these possible 
reactions are thought to be limited to certain clearly defined 
alternatives, while in the less explicit judgments they are 
not so clearly brought out. Throughout the various forms 
of judgment, from the most complex and deliberate down to 



156 Studies in Logical Theory 

the most simple and immediate, we found that a process 
could be traced which was like in kind and varied only in 
degree. And, finally, in the most immediate judgments 
where some of these features seem to disappear, the same 
account not only appears to be the most reasonable one, but 
there is the additional consideration, from the psychological 
side, that were not the judgment of this doubtful, tentative 
character, it would be difficult to understand how there could 
be judgment as distinct from a reflex. It appears, then, that 
throughout, the predicate is essentially of the nature of a 
hypothesis for dealing with the subject-matter. And, how- 
ever simple and immediate, or however involved and pro- 
longed, the judgment may be, it is to be regarded as 
essentially a process of reconstruction which aims at the 
resumption of an interrupted experience ; and when experi- 
ence has become itself a consciously intellectual affair, at the 
restoration of a unified objective situation. 

II 

Criticism of certain views concerning the hypothesis. — 
The explanation we have given of the hypothesis will enable 
us to criticise the treatment it has received from the 
empirical and the rationalistic schools. We shall endeavor 
to point out that these schools have, in spite of their opposed 
views, an assumption in common — something given in a 
fixed, or non-instrumental way ; and that consequently the 
hypothesis is either impossible or else futile. 

Bacon is commonly recognized as a leader in the reac- 
tionary inductive movement, which arose with the decline 
of scholasticism, and will serve as a good example of the 
extreme empirical position. In place of authority and the 
deductive method, Bacon advocated a return to nature and 
induction from data given through observation. The new 
method which he advanced has both a positive and a 



The Nature of Hypothesis 157 

negative side. Before any positive steps can be taken, the 
mind must be cleared of the various false opinions and 
prejudices that have been acquired. This preliminary task 
of freeing the mind from "phantoms," or "eidola," which 
Bacon likened to the cleansing of the threshing-floor, having 
been accomplished, nature should be carefully interrogated. 
There must be no hasty generalization, for the true method 
"collects axioms from sense and particulars, ascending con- 
tinuously and by degrees, so that in the end it arrives at 
the most general axioms." These axioms of Bacon's are 
generalizations based on observation, and are to be applied 
deductively, but the distinguishing feature of Bacon's 
induction is its carefully graduated steps. Others, too, had 
proceeded with caution (for instance Galileo), but Bacon laid 
more stress than they on the subordination of steps. 

It is evident that Bacon left very little room for hypothe- 
ses, and this is in keeping with his aversion to anticipa- 
tion of nature by means of "phantoms" of any sort; he 
even said explicitly that " our method of discovery in science 
is of such a nature that there is not much left to acuteness 
and strength of genius, but all degrees of genius and intel- 
lect are brought nearly to the same level." 1 Bacon gave no 
explanation of the function of the hypothesis ; in his opinion 
it had no lawful place in scientific procedure and must be 
banished as a disturbing element. Instead of the recipro- 
cal relation between hypothesis and data, in which hypothe- 
sis is not only tested in experience, but at the same time 
controls in a measure the very experience which tests it, 
Bacon would have a gradual extraction of general laws from 
nature through direct observation. He is so afraid of the 
distorting influence of conception that he will have nothing 
to do with conception upon any terms. So fearful is he of 
the influence of pre-judgment, of prejudice, that he will have 

i Novum Organum, Vol. I, p. 61. 



158 Studies in Logical Theory 

no judging which depends upon ideas, since the idea 
involves anticipation of the fact. Particulars are some- 
how to arrange and classify themselves, and to record or 
register, in a mind free from conception, certain generaliza- 
tions. Ideas are to be registered derivatives of the given 
particulars. This view is the essence of empiricism as a 
logical theory. If the views regarding the logic of thought 
before set forth are correct, it goes without saying that such 
empiricism is condemned to self-contradiction. It endeavors 
to construct judgment in terms of its subject alone; and 
the subject, as we have seen, is always a co-respondent to a 
predicate — an idea or mental attitude or tendency of intellec- 
tual determination. Thus the subject of judgment can be deter- 
mined only with reference to a corresponding determination 
of the predicate. Subject and predicate, fact and idea, are con- 
temporaneous, not serial in their relations (see pp. 110-12). 

Less technically the failure of Bacon's denial of the worth 
of hypothesis — which is in such exact accord with empiri- 
cism in logic — shows itself in his attitude toward experi- 
mentation and toward observation. Bacon's neglect of 
experimentation is not an accidental oversight, but is bound 
up with his view regarding the worthlessness of conception 
or anticipation. To experiment means to set out from an 
idea as well as from facts, and to try to construe, or even to 
discover, facts in accordance with the idea. Experimenta- 
tion not only anticipates, but strides to make good an antici- 
pation. Of course, this struggle is checked at every point 
by success or failure, and thus the hypothesis is continuously 
undergoing in varying ratios both confirmation and transfor- 
mation. But this is not to make the hypothesis secondary to 
the fact. It is simply to remain true to the proposition that 
the distinction and the relationship of the two is a thoroughly 
contemporaneous one. But it is impossible to draw any 
fixed line between experimentation and scientific observa- 



The Nature of Hypothesis 159 

tions. To insist upon the need of systematic observation 
and collection of particulars is to set up a principle which is 
as distinct from the casual accumulation of impressions as 
it is from nebulous speculation. If there is to be observa- 
tion of a directed sort, it must be with reference to some 
problem, some doubt, and this, as we have seen, is a stimu- 
lus which throws the mind into a certain attitude of response. 
Controlled observation is inquiry, it is search; consequently 
it must be search for something. Nature cannot answer 
interrogations excepting as such interrogations are put; and 
the putting of a question involves anticipation. The observer 
does not inquire about anything or look for anything except- 
ing as he is after something. This search implies at once 
the incompleteness of the particular given facts, and the 
possibility — that is ideal — of their completion. 

It was not long until the development of natural science 
compelled a better understanding of its actual procedure 
than Bacon possessed. Empiricism changed to experimen- 
talism. With experimentalism inevitably came the recog- 
nition of hypotheses in observing, collecting, and comparing 
facts. It is clear, for instance, that Newton's fruitful investi- 
gations are not conducted in accordance with the Baconian 
notion. It is quite clear that his celebrated four rules for 
philosophizing 1 are in truth statements of certain principles 
which are to be observed in forming hypotheses. They 
imply that scientific technique had advanced to a point 

iNewton's " Rules for Philosophizing " (Principia, Book III) are as follows: 

Rule I. " No more causes of natural things are to be admitted than such as are 
both true, and sufficient to explain the phenomena of those things." 

Rule II. " Natural effects of the same kind are to be referred as far as possible 
to the same causes. ' 

Rule III. " Those qualities of bodies that can neither be increased nor dimin- 
ished in intensity, and which are found to belong to all bodies within reach of our 
experiments are to be regarded as qualities of all bodies whatever." 

Rule IV. "In experimental philosophy propositions collected by induction 
from phenomena are to be regarded either as accurately true or very nearly true 
notwithstanding any contrary hypothesis, till other phenomena occur, by which they 
are made more accurate, or are rendered subject to exceptions." 



160 Studies in Logical Theoky 

where hypotheses were such regular and indispensable fac- 
tors that certain uniform conditions might be laid down for 
their use. The fourth rule in particular is a statement of 
the relative validity of hypothesis as such until there is 
ground for entertaining a contrary hypothesis. 

The subsequent history of logical theory in England is 
conditioned upon its attempt to combine into one system the 
theories of empiristic logic with recognition of the procedure 
of experimental science. This attempt finds its culmination 
in the logic of John Stuart Mill. Of his interest in and 
fidelity to the actual procedure of experimental science, as 
he saw it, there can be no doubt. Of his good faith in con- 
cluding his Introduction with the words following there can 
be no doubt: "I can conscientiously affirm that no one 
proposition laid down in this work has been adopted for the 
sake of establishing, or with any reference for its fitness in 
being employed in establishing, preconceived opinions in 
any department of knowledge or of inquiry on which the 
speculative world is still undecided." Yet Mill was equally 
attached to the belief that ultimate reality, as it is for the 
human mind, is given in sensations, independent of ideas ; 
and that all valid ideas are combinations and convenient 
ways of using such given material. Mill's very sincerity made 
it impossible that this belief should not determine, at every 
point, his treatment of the thinking process and of its various 
instrumentalities. 

In Book III, chap. 14, Mill discusses the logic of expla- 
nation, and in discussing this topic naturally finds it neces- 
sary to consider the matter of the proper use of scientific 
hypotheses. This is conducted from the standpoint of their 
use as that is reflected in the technique of scientific dis- 
covery. In Book IV, chap. 2, he discusses "Abstraction or 
the Formation of Conceptions " — a topic which obviously 
involves the forming of hypotheses. In this chapter, his con- 



The Nature of Hypothesis 161 

sideration is conducted in terms, not of scientific procedure, 

but of general philosophical theory, and this point of view 

is emphasized by the fact that he is opposing a certain view 

of Dr. Whewell. 

The contradiction between the statements in the two 

chapters will serve to bring out the two points already made, 

viz., the correspondent character of datum and hypothesis, 

and the origin of the latter in a problematic situation and its 

consequent use as an instrument of unification and solution. 

Mill first points out that hypotheses are invented to enable 

the deductive method to be applied earlier to phenomena ; 

that it does this by suppressing the first of the three steps, 

induction, ratiocination, and verification. He states that : 

The process of tracing regularity in any complicated, and at 
first sight confused, set of appearances is necessarily tentative; we 
begin by making any supposition, even a false one, to see what con- 
sequences will follow from it; and by observing how these differ 
from the real phenomena, we learn what corrections to make in our 

assumption Neither induction nor deduction would enable 

us to understand even the simplest phenomena, if we did not 
often commence by anticipating the results; by making a provi- 
sional supposition, at first essentially conjectural, as to some of the 
very notions which constitute the final object of the inquiry. 1 

If in addition we recognize that, according to Mill, our 
direct experience of nature always presents us with a compli- 
cated and confused set of appearances, we shall be in no 
doubt as to the importance of ideas as anticipations of a pos- 
sible experience not yet had. Thus he says: 

The order of nature, as perceived at a first glance, presents at 
every instant a chaos followed by another chaos. We must decom- 
pose each chaos into single facts. We must learn to see in the 
chaotic antecedent a multitude of distinct antecedents, in the cha- 
otic consequent a multitude of distinct consequents. 2 

iBook III, chap. 2, sec. 5; italics mine. The latter part of the passage, begin- 
ning with the words " If we did not often commence," etc., is quoted by Mill from 
Comte. The words " neither induction nor deduction would enable us to understand 
even the simplest phenomena 1 ' are his own. 

2 Book III, chap. 7, sec. 1. 



1&2 Studies in Logical Theoey 

In the next section of the same chapter he goes on to state 
that, having discriminated the various antecedents and con- 
sequents, we then " are to inquire which is connected with 
which." This requires a still further resolution of the complex 
and of the confused. To effect this we must vary the cir- 
cumstances; we must modify the experience as given with 
reference to accomplishing our purpose. To accomplish 
this purpose we have recourse either to observation or to 
experiment: "We may either find an instance in nature 
suited to our purposes, or, by an artificial arrangement of 
circumstances, make one" (the italics in "suited to our pur- 
pose" are mine; the others are Mill's). He then goes on to 
say that there is no real logical distinction between observa- 
tion and experimentation. The four methods of experimen- 
tal inquiry are expressly discussed by Mill in terms of their 
worth in singling out and connecting the antecedents and 
consequents which actually belong together, from the chaos 
and confusion of direct experience. 

We have only to take these statements in their logical 
connection with each other (and this connection runs through 
the entire treatment by Mill of scientific inquiry), to recog- 
nize the absolute necessity of hypothesis to undertaking any 
directed inquiry or scientific operation. Consequently we 
are not surprised at finding him saying that "the function 
of hypotheses is one which must be reckoned absolutely 
indispensable in science;" and again that " the hypothesis 
by suggesting observations and experiments puts us on the 
road to independent evidence." 1 

Since Mill's virtual retraction, from the theoretical point 
of view, of what is here said from the standpoint of scientific 
procedure, regarding the necessity of ideas is an accompani- 
ment of his criticism of Whewell, it will put the discussion 
in better perspective if we turn first to Whewell's views. 2 

1 Book III, chap. 14, sees. 4 and 5. 

2 William Whewell, The Philosophy of the Inductive Sciences, London, 1840. 



The Nature of Hypothesis 163 

The latter began by stating a distinction which easily might 
have been developed into a theory of the relation of fact and 
idea which is in line with that advanced in this chapter, and 
indeed in this volume as a whole. He questions (chap. 2) 
the fixity of the distinction between theory and practice. 
He points out that what we term facts are in effect simply 
accepted inferences; and that what we call theories are 
describable as facts, in proportion as they become thoroughly 
established. A true theory is a fact. "All the great theories 
which have successively been established in the world are 
now thought of as facts." "The most recondite theories 
when firmly established are accepted as facts; the simplest 
facts seem to involve something of the nature of theory." 

The conclusion is that the distinction is a historic one, 
depending upon the state of knowledge at the time, and 
upon the attitude of the individual. What is theory for one 
epoch, or for one inquirer in a given epoch, is fact for some 
other epoch, or even for some other more advanced inquirer 
in the same epoch. It is theory when the element of infer- 
ence involved in judging any fact is consciously brought 
out; it is fact when the conditions are such that we have 
never been led to question the inference involved, or else, 
having questioned it, have so thoroughly examined into the 
inferential process that there is no need of holding it further 
before the mind, and it relapses into unconsciousness again. 
" If this greater or less consciousness of our own internal act 
be all that distinguishes fact from theory, we must allow that 
the distinction is still untenable " (untenable, that is to say, 
as a fixed separation). Again, "fact and theory have no 
essential difference except in the degree of their certainty 
and familiarity. Theory, when it becomes firmly estab- 
lished and steadily lodged in the mind becomes fact." (P. 45; 
italics mine.) And, of course, it is equally true that as fast 
as facts are suspected or doubted, certain aspects of them 



164 Studies in Logical Theory 

are transferred into the class of theories and even of mere 
opinions. 

I say this conception might have been developed in a 
way entirely congruous with the position of this chapter. 
This would have happened if the final distinction between 
fact and idea had been formulated upon the basis simply of 
the points, " relative certainty and familiarity." From 
this point of view the distinction between fact and idea is 
one purely relative to the doubt-inquiry function. It has 
to do with the evolution of an experience as regards its con- 
scious surety. It has its origin in problematic situations. 
Whatever appears to us as a problem appears as contrasted 
with a possible solution. Whatever objects of thought refer 
particularly to the problematic side are theories, ideas, 
hypotheses ; whatever relates to the solution side is surety, 
unquestioned familiarity, fact. This point of view makes 
the distinctions entirely relative to the exigencies of the pro- 
cess of reflective transformation of experience. 

Whewell, however, had no sooner started in this train of 
thought than he turns his back upon it. In chap. 3' he trans- 
forms what he had proclaimed to be a relative, historic, and 
working distinction into a fixed and absolute one. He 
distinguishes between sensations and ideas, not upon a 
genetic basis with reference to establishing the conditions 
of further operation ; but with reference to a fundamentaHy 
fixed line of demarkation between what is passively given to 
the mind and the activity put forth by the mind. Thus he 
reinstates in its most generalized and fixed, and therefore 
most vicious, form the separation which he has just rejected. 
Sensations are a brute unchangeable element of fact which 
exists and persists independent of ideas; an idea is a 
mode of mental operation which occurs and recurs in an 
independent individuality of its own. If he had carried out 
the line of thought with which he began, sensation as fact 



The Nature of Hypothesis 165 

would have been that residuum of familiarity and certainty 
which cannot be eliminated, however much else of an expe- 
rience is dissolved in the inner conflict. Idea as hypothe- 
sis or theory would have been the corresponding element 
in experience which is necessary to redintegrate this resi- 
duum into a coherent and significant experience. 

But since Whewell did not follow out his own line of 
thought, choosing rather to fall back on the Kantian anti- 
thesis of sense and thought, he had no sooner separated his 
fact and idea, his given datum and his mental relation, than 
he is compelled to get them together again. The idea be- 
comes "a general relation which is imposed upon perception 
by an act of the mind, and which is different from anything 
which our senses directly offer to us" (p. 26). Such con- 
ceptions are necessary to connect the facts which we learn 
from our senses into truths. "The ideal conception which 
the mind itself supplies is superinduced upon the facts as 
they are originally presented to observation. Before the 
inductive truth is detected, the facts are there, but they are 
many and unconnected. The conception which the dis- 
coverer applies to them gives them connection and unity." 
(P. 42.) All induction, according to Whewell, thus depends 
upon superinduction — imposition upon sensory data of cer- 
tain ideas or general relations existing independently in 
the mind. 1 

We do not need to present again the objections already 
offered to this view: the impossibility of any orderly stimu- 
lation of ideas by facts, and the impossibility of any check 
in the imposition of idea upon fact. "Facts" and concep- 
tion are so thoroughly separate and independent that any 
sensory datum is indifferently and equally related to any 
conceivable idea. There is no basis for " superinducing" 

1 The essential similarity between WhewelTs view and that of Lotze, already dis- 
cussed (see chap. 3) is of course explainable on the basis of their common relation- 
ship to Kant. 



166 Studies in Logical Theoby 

one idea or hypothesis, rather than any other, upon any 
particular set of data. 

In the chapter already referred to upon abstraction, or 
the formation of conceptions, Mill seizes upon this difficulty. 
Yet he and Whewell have one point in common: they both 
agree in the existence of a certain subject-matter which is 
given for logical purposes quite outside of the logical pro- 
cess itself. Mill agrees with Whewell in postulating a 
raw material of pure sensational data. In criticising Whew- 
ell's theory of superinduction of idea upon fact, he is 
therefore led to the opposite assertion of the complete depend- 
ence of ideas as such upon the given facts as such — in 
other words, he is led to a reiteration of the fundamental 
Baconian empiricism; and thus to a virtual retraction of 
what he had asserted regarding the necessity of ideas to 
fruitful scientific inquiry, whether in the way of observa- 
tion or experimentation. The following quotation gives a 
fair notion of the extent of Mill's retraction: 

The conceptions then which we employ for the colligation and 
methodization of facts, do not develop themselves from within, but 
are impressed upon the mind from without; they are never ob- 
tained otherwise than by way of comparison and abstraction, and, 
in the most important and most numerous cases, are evolved by ab- 
straction from the very phenomena which it is their office to colli- 
gate} 

Even here Mill's sense for the positive side of scientific in- 
quiry suffices to reveal to him that the "facts" are some- 
how inadequate and defective, and are in need of assistance 
from ideas — and yet the ideas which are to help out the 
facts are to be the impress of the unsure facts! The con- 
tradiction comes out very clearly when Mill says: "The 
really difficult cases are those in which the conception des- 
tined to create light and order out of darkness and confu- 

i Logic, Book IV, chap. 2, sec. 2 ; italics mine. 



The Nature of Hypothesis 167 

sion has to be sought for among the very phenomena which 
it afterward serves to arrange." 1 

Of course, there is a sense in which Mill's view is very 
much nearer the truth than is Whewell's. Mill at least sees 
that " idea " must be relevant to the facts or data which it is 
to arrange, which are to have "light and order" introduced 
into them by means of the idea. He sees clearly enough 
that this is impossible save as the idea develops within the 
same experience in which the "dark and confused" facts are 
presented. He goes on to show correctly enough how con- 
flicting data lead the mind to a "confused feeling of an 
analogy " between the data of the confused experience and 
of some other experience which is orderly (or already colli- 
gated and methodized) ; and how this vague feeling, through 
processes of further exploration and comparison of experi- 
ences, gets a clearer and more adequate form until we finally 
accept it. He shows how in this process we continually 
judge of the worth of the idea which is in process of forma- 
tion, by reference to its appropriateness to our purpose. He 
goes so far as to say : " The question of appropriateness is 
relative to the particular object we have in view" 2 He sums 
up his discussion by stating: "We cannot frame good gen- 
eral conceptions beforehand. That the conception we have 
obtained is the one we want can only be known when we have 
done the work for the sake of which we wanted it." 3 

This all describes the actual state of the case, but it is 
consistent only with a logical theory which makes the dis- 
tinction between fact and hypothesis instrumental in the 
tiansformation of experience from a confused into an organ- 
ized form; not with Mill's notion that sensations are some- 
how finally and completely given as ultimate facts, and 

Ubid. 

2 Ibid., sec. 4; in sec. 6 he states even more expressly that any conception is ap- 
propriate in the degree in which it " helps us toward what we wish to understand." 

3 Ibid., sec. 6 ; italics mine. * 



168 Studies in Logical Theory 

that ideas are mere re-registrations of such facts. It is 
perfectly just to say that the hypothesis is impressed upon 
the mind (in the sense that any notion which occurs to the 
mind is impressed) in the course of an experience. It is 
well enough, if one define what he means, to say that the 
hypothesis is impressed (that is to say, occurs or is sug- 
gested) through the medium of given facts, or even of sen- 
sations. But it is equally true that the facts are presented 
and that sensations occur within the course of an experience 
which is larger than the bare facts, because involving the 
conflicts among them and the corresponding intention to 
treat them in some fashion which will secure a unified expe- 
rience. Facts get power to suggest ideas to the mind — to 
" impress" — only through their position in an entire expe- 
rience which is in process of disintegration and of recon- 
struction — their "fringe" or feeling of tendency is quite 
as factual as they are. The fact that "the conception we 
have obtained is the one we want can be known only when 
we have done the work for the sake of which we wanted it," 
is enough to show that it is not bare facts, but facts in rela- 
tion to want and purpose and purpose in relation to facts, 
which originate the hypothesis. 

It would be interesting to follow the history of discus- 
sion of the hypothesis since the time of Whewell and of Mill, 
particularly in the writings of Jevons, Venn, and Bosanquet. 
This history would refine the terms of our discussion by 
introducing more complex distinctions and relations. But 
it would be found, I think, only to refine, not to introduce 
any fundamentally new principles. In each case, we find the 
writer struggling with the necessity of distinguishing 
between fact and idea; of giving the fact a certain primacy 
with respect to testing of idea and of giving the idea a primacy 
with respect to the significance and orderliness of the fact; 
and of holding throughout to a relationship of idea with 



The Nature of Hypothesis 169 

fact so intimate that the idea develops only by being "com- 
pared " with facts (that is, used in construing them), and facts 
get to be known only as they are " connected " through the 
idea — and we find that what is a maze of paradoxes and 
inconsistencies from an absolute, from a non-historic stand- 
point, is a matter of course the moment it is looked at from 
the standpoint of experience engaged in self -transformation 
of meaning through conflict and reconstitution. 

But we can only note one or two points. Jevons's "infi- 
nite ballot-box " of nature which is absolutely neutral as to 
any particular conception or idea, and which accordingly 
requires as its correlate the formation of every possible hy- 
pothesis (all standing in themselves upon the same level of 
probability) is an interesting example of the logical conse- 
quences of feeling the need of both fact and hypothesis for 
scientific procedure and yet regarding them as somehow 
arising independently of each other. It is an attempt to 
combine extreme empiricism and extreme rationalism. The 
process of forming hypotheses and of deducing their rational 
consequences goes on at random, because the disconnectedness 
of facts as given is so ultimate that the facts suggest one hypo- 
thesis no more readily than another. Mathematics, in its two 
forms of measurements as applied to the facts, and of calcula- 
tion as applied in deduction, furnishes Jevons the bridge by 
which he finally covers the gulf which he has first himself cre- 
ated. Venn's theory requires little or no restatement to bring 
it into line with the position taken in the text. He holds to 
the origin of hypothesis in the original practical needs of 
mankind, and to its gradual development into present scien- 
tific form. 1 He states expressly: 

The distinction between what is known and what is not 
known is essential to Logic, and peculiarly characteristic of it 
in a degree not to be found in any other science. Inference is the 

i Venn, Empirical Logic, p. 383. 



170 Studies in Logical Theory 

process of passing from one to the other; from facts which we had 
accepted as premises, to those which we have not yet accepted, 
but are in the act of doing so by the very process in question. Xo 
scrutiny of the facts themselves, regarded as objective, can ever 
detect these characteristics of' their greater or less familiarity to 
our minds. We must introduce also the subjective element if we 
wish to give any adequate explanation of them. 1 

Venn, however, does not attempt a thoroughgoing state- 
ment of logical distinctions, relations, and operations, as 
parts "of the act of passing from the unknown to the known." 
He recognizes the relation of reflection to a historic process, 
which we have here termed " reconstruction," and the origin 
and worth of hypothesis as a tool in the movement, but does 
not carry Iris analysis to a systematic form. 

Ill 

Origin of the hypothesis. — In our analysis of the process 
of judgment, we attempted to show that the predicate arises 
in case of failure of some line of activity going on in terms 
of an established habit. When the old habit is checked 
through failure to deal with new conditions (i. e., when the 
situation is such as to stimulate two habits with distinct 
aims) the problem is to find a new method of response — 
that is, to co-ordinate the conflicting tendencies by building 
up a single aim which will function the existing situation. 
As we saw that, in case of judgment, habit when checked 
became ideal, an idea, so the new habit is first formalized as 
an ideal type of reaction and is the hypothesis by which we 
attempt to construe new data. In our inquiry as to how this 
formulation is effected, i. e. , how the hypothesis is developed, 
it will be convenient to take some of the currently accepted 
statements as to their origin, and show how these statements 
stand in reference to the analysis proposed. 

1 Venn, Empirical Logic, p. 25; italics mine. 



The Nature of Hypothesis 171 



ST/fcOT: 



Enumerative induction and allied processes. — It is 
pointed out by Wei ton 1 that the various ways in which 
hypotheses are suggested may be reduced to three classes, 
viz., enumerative induction, conversion of propositions, and 
analogy. Under the head of "enumeration" he reminds us 
that "every observed regularity of connection between phe- 
nomena suggests a question as to whether it is universal." 
There are numerous instances of this in mathematics. For 
example, it is noticed that 1 + 3 = 2 2 , 1 + 3 + 5 = 3 2 , 1 + 3 + 
5 + 7=4 2 , etc.; and one is led to ask whether there is any 
general principle involved, so that the sum of the first n odd 
numbers will be n 2 , where n is any number, however great. 
In this early form of inductive inference there are two diver- 
gent tendencies. One is the tendency to complete enumera- 
tion. This tendency is clearly ideal — it transcends the facts 
as given. To look for all the cases is thus itself an experi- 
mental inquiry, based upon a hypothesis which it endeavors 
to test. But in most cases enumeration can be only incom- 
plete, and we are able to reach nothing better than proba- 
bility. Hence the other tendency in the direction of an 
analysis of content in search for a principle of connection in 
the elements in any one case. For if a characteristic belong- 
ing to a number of individuals suggests a class where it 
belongs to all individuals, it must be that it is found in 
every individual as such. The hypothesis of complete class 
involves a hypothesis as to the character of each individual 
in the class. Thus a hypothesis as to extension transforms 
itself into one as to intension. 

But it is analogy which Welton considers "the chief 
source from which new hypotheses are drawn." In the 
second tendency mentioned under enumerative induction, 
that is, the tendency to analysis of content or intension, we 
are naturally led to analogy, for in our search for the char- 

i Welton, Manual of Logic, Vol. II, chap. 3. 



172 Studies in Logical Theory 

acteristic feature which determines classification among the 
concrete particulars our first step will be an inference by- 
analogy. In analogy attention is turned from the number 
of observed instances to their character, and, because par- 
ticulars have some feature in common, they are supposed to 
be the same in still other respects. While the best we can 
reach in analogy is probability, the arguments may be such 
as to result in a high degree of certainty. The form of the 
argument is valuable in so far as we are able to distinguish 
between essential and nonessential characteristics on which 
to base our analogy. What is essential and what nonessen- 
tial depends upon the particular end we have in view. 

In addition to enumerative induction, which Welton has 
mentioned, it is to be noted that there are a number of other 
processes which are very similar to it in that a number of 
particulars appear to furnish a basis for a general principle 
or method. Such instances are common in induction, in 
instruction, and in methods of proof. 

If one is to be instructed in some new kind of labor, he 
is supposed to acquire a grasp of the method after having 
been shown in a few instances how this particular work is to 
be done; and, if he performs the manipulations himself, so 
much the better. It is not asked why the experience of a 
few cases should be of any assistance, for it seems self- 
evident that an experienced man, a man who has acquired 
the skill, or knack, of doing things, should deal better with 
all other cases of similar nature. 

There is something very similar in inductive proofs, as 
they are called. The inductive proof is common in algebra. 
Suppose we are concerned in proving the law of expansion 
of the binomial theorem. We show by actual calculation 
that, if the law holds good for the nth power, it is true for 
the 11 + first power. That is, if it holds for any power, it 
holds for the next also. But we can easilv show that it does 



The Nature of Hypothesis 173 

hold for, say, the second power. Then it must be true for 
the third, and hence for the fourth, and so on. Whether 
this law, though discovered by inductive processes, depends 
on deduction for the conclusiveness of its proof, as Jevons 
holds; 1 whether, as Erdmann 2 contends, the proof is thor- 
oughly deductive; or whether Wundt 3 is right in maintain- 
ing that it is based on an exact analogy, while the 
fundamental axioms of mathematics are inductive, it is clear 
that in such proofs a few instances are employed to give the 
learner a start in the right direction. Something suggests 
itself, and is found true in this case, in the next, and again 
in the next, and so on. It may be questioned whether there 
is usually a very clear notion of what is involved in the "so 
on." To many it appears to mark the point where, after 
having been taken a few steps, the learner is carried on by 
the acquired momentum somewhat after the fashion of one 
of Newton's laws of motion. Whether the few successive 
steps are an integral part of the proof or merely serve as 
illustration, they are very generally resorted to. In fact, 
they are often employed where there is no attempt to intro- 
duce a general term such as n, or k, or Z, but the few indi- 
vidual instances are deemed quite sufficient. Such, for 
instance, is the custom in arithmetical processes. We call 
attention to these facts in order to show that successive 
cases are utilized in the course of explanation as an aid in 
establishing the generality of a law. 

In geometry we find a class of proofs in which the suc- 
cessive steps seem to have great significance. A common 
proof of the area of the circle will serve as a fair example. 
A regular polygon is circumscribed about the circle. Then 
as the number of its sides are increased its area will approach 

i W. S. Jevons, Principles of Science, pp. 231, 232. 

2B. Erdmann, "Zur Theorie des Syllogismus und der Induktion," Philoso- 
phische Abhandlungen, Vol. VI, p. 230. 

3 Wundt, Logik, 2d ed., Vol. II, p. 131. 



174 Studies in Logical Theory 

that of the circle, as its perimeter approaches the circumfer- 
ence of the circle. The area of the circle is thus inferred to 
be 77- _R 2 , since the area of the polygon is always -J _Rx perim- 
eter, and in case of the circle the circumference =2irR. 
Here again we get under such headway by means of the 
polygon that we arrive at the circle with but little difficulty. 
Had we attempted the transition at once, say, from a cir- 
cumscribed square, we should doubtless have experienced 
some uncertainty and might have recoiled from what would 
seem a rash attempt; but as the number of the sides of our 
polygon approach infinity — that mysterious realm where 
many paradoxical things become possible — the transition 
becomes so easy that our polygon is often said to have truly 
become a circle. 

Similarly, some statements of the infinitesimal calculus 
rest on the assumption that slight degrees of difference may 
be neglected. Though the more modern theory of limits 
has largely displaced this attitude in calculus and has also 
changed the method of proof in such geometrical problems 
as the area of the circle, the underlying motive seems to 
have been to make transitions easy, and thus to make possible 
a continued application of some particular method or way of 
dealing with things. 

But granted that this is all true, what has it to do with 
the origin of the hypothesis? It seems likely that the 
hypothesis may be suggested by a few successive instances ; 
but are these to be classed with the successive steps in proof 
to which we have referred? In the first place, we attempt 
to prove our hypothesis because we are not sure it is true; 
we are not satisfied that there are no other tenable hypothe- 
ses. But if we do test it, is not such test enough? It 
depends upon how thorough a grasp we have of the situa- 
tion; but, in general, each test case adds to its probability. 
The value of tests lies in the fact that they strengthen and 



The Nature of Hypothesis 175 

tend to confirm our hypothesis by checking the force of 
alternatives. One instance is not sufficient because there 
are other possible incipient hypotheses, or more properly 
tendencies, and the enumeration serves to bring one of these 
tendencies into prominence in that it diminishes other vague 
and perhaps subconscious tendencies and strengthens the 
one which suddenly appears as the mysterious product of 
genius. 

The question might arise why the mere repetition of con- 
flicting tendencies would lead to a predominance of one of 
them. Why would they not all remain in conflict and con- 
tinue to check any positive result? It is probably because 
there never is any absolute equilibrium. The successive 
instances tend to intensify and bring into prominence some 
tendency which is already taking a lead, so to speak. And 
it may be said further in this connection that only as seen 
from the outside, only as a mechanical view is taken, does 
there appear to be an excluding of definitely made out alter- 
natives. 

In explanation of the part played by analogy in the origin 
of hypotheses, Welton points out that a mere number of 
instances do not take us very far, and that there must be 
some " specification of the instances as well as numbering of 
them," and goes on to show that the argument by enumera- 
tive induction passes readily into one from analogy, as soon 
as attention is turned from the number of the observed 
instances to their character. It is not necessary, however, 
to pass to analogy through enumerative induction. " When 
the instances presented to observation offer immediately the 
characteristic marks on which we base the inference to the 
connection of S and P, we can proceed at once to an infer- 
ence from analogy, without any preliminary enumeration of 
the instances." 1 

i Welton, Manual of Logic, Vol. II, p. 72. 



176 Studies in Logical Theory 

Welton, and logicians generally, regard analogy as an 
inference on the basis of partial identity. Because of cer- 
tain common features we are led to infer a still greater like- 
ness. 

Both enumerative induction and analogy are explicable 
in terms of habit. We saw in our examination of enume- 
rative induction that a form of reaction gains strength 
through a series of successful applications. Analogy marks 
the presence of an identical element together with the ten- 
dency to extend this "partial identity" (as it is commonly 
called) still farther. In other words, in analogy it is sug- 
gested that a type of reaction which is the same in certain 
respects may be made similar in a greater degree. In enu- 
merative induction we lay stress on the number of instances 
in which the habit is applied. In analogy we emphasize the 
content side and take note of the partial identity. In fact, 
the relation between enumerative induction and analogy is 
of the same sort as that existing between association by con- 
tiguity and association by similarity. In association by 
contiguity we think of the things associated as merely stand- 
ing in certain temporal or spatial relations, and disregard the 
fact that they were elements in a larger experience. In case 
of association by similarity we regard the like feature in the 
things associated as a basis for further correction. 

In conversion of propositions we try to reverse the direc- 
tion of the reaction, so to speak, and thereby to free the habit, 
to get a mode of response so generalized as to act with a 
minimum cue. For instance, we can deal with A in a 
way called B, or, in other words, in the same way that 
we did with other things called B. If we say, "Man is 
an animal," then to a certain extent the term "animal" 
signifies the way in which we regard "man." But the 
question arises whether we can regard all animals as we 
do man. Evidently not, for the reaction which is fitting in 



The Nature of Hypothesis 177 

case of animals would be only partially applicable to man. 
With the animals that are also men we have the beginning 
of a habit which, if unchecked, would lead to a similar reac- 
tion toward all animals, i. e., we would say: "All animals 
are men." Man may be said to be the richer concept, in 
that only a part of the reaction which determines an object 
to be a man is required to designate it as an animal. On 
the other hand, if we start with animal, then (except in case 
of the animals which are men) there is lacking the subject- 
matter which would permit the fuller concept to be applied. 
By supplying the conditions under which animal == man we 
get a reversible habit. The equation of technical science has 
just this character. It represents the maximum freeing or 
abstraction of a predicate qua predicate, and thereby multi- 
plies the possible applications of it to subjects of future 
judgments, and lessens the amount of shearing away of 
irrelevancies and of re-adaptation necessary when so used 
in any particular case. 

Formation and test of the hypothesis. — The formation of 
the hypothesis is commonly regarded as essentially different 
from the process of testing, which it subsequently under- 
goes. We are said to observe facts, invent hypotheses, and 
then test them. The hypothesis is not required for our pre- 
liminary observations; and some writers, regarding the 
hypothesis as a formulation which requires a difficult and 
elaborate test, decline to admit as hypotheses those more 
simple suppositions, which are readily confirmed or rejected. 
A very good illustration of this point of view is met with in 
Wundt's discussion of the hypothesis, by an examination of 
which we hope to show that such distinctions are rather arti- 
ficial than real. 

The subject-matter of science, says Wundt, 1 is constituted 
by that which is actually given and that which is actually to 

l Op. cit., Vol. I, p. 452 ff. 



178 Studies in Logical Theoey 

be expected. The whole content is not limited to this, 
however, for these facts must be supplemented by certain 
presuppositions, which are not given in a factual sense. 
Such presuppositions are called hypotheses and are justified 
by our fundamental demand for unity. However valuable 
the hypothesis may be when rightly used, there is constant 
danger of illegitimately extending it by additions that spring 
from mere inclinations of fancy. Furthermore, the hypothe- 
sis in this proper scientific sense must be carefully dis- 
tinguished from the various inaccurate uses, which are 
prevalent. For instance, hypotheses must not be confused 
with expectations of fact. As cases in point Wundt men- 
tions Galileo' s suppositions that small vibrations of the 
pendulum are isochronous, and that the space traversed by 
a falling body is proportional to the square of the time it 
has been falling. It is true that such anticipations play an 
important part in science, but so long as they relate to the 
facts themselves or to their connections, and can be con- 
firmed or rejected any moment through observation, they 
should not be classed with those added presuppositions 
which are used to co-ordinate facts. Hence not all supposi- 
tions are hypotheses. On the other hand, not every 
hypothesis can be actually experienced. For example, one 
employs in physics the hypothesis of electric fluid, but does 
not expect actually to meet with it. In many cases, how- 
ever, the hypothesis becomes proved as an experienced fact. 
Such was the course of the Copernican theory, which was at 
first only a hypothesis, but was transformed into fact 
through the evidence afforded by subsequent astronomical 
observation. 

Wundt defines a theory as a hypothesis taken together 
with the facts for whose elucidation it was invented. In 
thus establishing a connection between the facts which the 
hypothesis merely suggested, the theory furnishes at the 



The Nature of Hypothesis 179 

same time partly the foundation (Begrilndung) and partly 
the confirmation (Bestdtigung) of the hypothesis. 1 These 
aspects, Wundt insists, must be sharply distinguished. 
Every hypothesis must have its Begrilndung, but there can 
be Bestdtigung only in so far as the hypothesis contains 
elements which are accessible to actual processes of verifica- 
tion. In most cases verification is attainable in only cer- 
tain elements of the hypothesis. For example, Newton was 
obliged to limit himself to one instance in the verification of 
his theory of gravitation, viz., the movements of the moon. 
The other heavenly bodies afforded nothing better than a 
foundation in that the supposition that gravity decreases as 
the square of the distance increases enabled him to deduce 
the movements of the planets. The main object of his 
theory, however, lay in the deduction of these movements 
and not in the proof of universal gravity. With the Dar- 
winian theory, on the contrary, the main interest is in seek- 
ing its verification through examination of actual cases of 
development. Thus, while the Newtonian and the greater 
part of the other physical theories lead to a deduction of 
the facts from the hypotheses, which can be verified only 
in individual instances, the Darwinian theory is concerned 
in evolving as far as possible the hypothesis out of the 
facts. 

Let us look more closely at Wundt' s position. We will 
ask, first, whether the distinction between hypotheses and 
expectations is as pronounced as he maintains; and, second, 
whether the relation between Begrilndung and Bestdtigung 
may not be closer than Wundt would have us believe. 

As examples of the hypothesis Wundt mentions the 
Copernican hypothesis, Newton's hypothesis of gravitation, 
and the predictions of the astronomers which led to the dis- 
covery of Neptune. As examples of mere expectations we 

i Op. cit., Vol. I, pp. 454-461. 



180 Studies in Logical Theory 

are referred to Galileo's experiments with falling bodies and 
pendulums. In case of Newton's hypothesis there was the 
assumption of a general law, which was verified after much 
labor and delay. The heliocentric hypothesis of Coperni- 
cus, which was invented for the purpose of bringing system 
and unity into the movements of the planets, has also been 
fairly well substantiated. In the discovery of Neptune we 
have, apparently, not the proof of a general law or the dis- 
covery of further peculiarities of previously known data, but 
rather the discovery of a new object or agent by means of 
its observed effects. In each of these instances we admit 
that the hypothesis was not readily suggested or easily 
and directly tested. 

If we turn to Galileo's pendulum and falling bodies, it is 
clear first of all that he did not have in mind the discovery 
of some object, as was the case in the discovery of Neptune. 
Did he, then, either contribute to the proof of a general law 
or discover further characteristics of things already known 
in a more general way? Wundt tells us that Galileo only 
determined a little more exactly what he already knew, and 
that he did this with but little labor or delay. 

What, then, is the real difference between hypothesis and 
expectation ? If we compare Galileo's determination of the 
law of falling bodies with Newton's test of his hypothesis of 
gravitation, we see that both expectation and hypothesis 
were founded on observation and took the form of mathe- 
matical formulse. Each tended to confirm the general law 
expressed in its formula, though there was, of course, much 
difference in the time and labor required. If we compare 
the Copernican hypothesis with Galileo's supposition con- 
cerning the pendulum, we find again that they agree in 
regard to general purpose and method, and differ in the 
difficulty of verification. If the experiment with the pen- 
dulum only substituted exactness for inexactness, did the 



The Nature of Hypothesis 181 

Copernican theory do anything different in kind ? It is true 
that the more exact statement of the swing of the pendulum 
was expressed in quantitative form, but quantitative state- 
ment is no criterion of either the presence or the absence of 
the hypothesis. 

Again, we may compare the pendulum with Kepler's laws. 
What was Kepler's hypothesis, that the square of the periodic 
times of the several planets are proportional to the cubes of 
their mean distances from the sun, except a more exact for- 
mulation of facts which were already known in a more gen- 
eral way ? Wundt's position seems to be this : whenever a 
supposition or suggestion can be tested readily, it should 
not be classed as a hypothesis. This would make the dis- 
tinction one of degree rather than kind, and it does not 
appear how much labor we must expend, or how long our 
supposition must evade our efforts to test it, before it can 
win the title of hypothesis. 

In the second place, we have seen that Wundt draws a 
sharp line between Begrilndung and Bestdtigung. It is 
doubtless true that every hypothesis requires a certain justi- 
fication, for unless other facts can be found which agree 
with deductions made in accordance with it, its only sup- 
port would be the data from which it is drawn. Such sup- 
port as this would be obtained through a process too clearly 
circular to be seriously entertained. The distinction which 
Wundt draws between Begrilndung and Bestdtigung is 
evidently due to the presence of the experimental element 
in the latter. For descriptive purposes this distinction is 
useful, but is misleading if it is understood to mean that 
there is mere experience in one case and mere inference in the 
other. The difference is rather due to the relative parts played 
by inference and by accepted experience in each. In Begriln- 
dung the inferential feature is the more prominent, while in 
Bestdtigung the main emphasis is on the experiential aspect. 



182 Studies in Logical Theoey 

It must not be supposed, however, that either of these 
aspects can be wholly absent. It is difficult to understand 
how any hypothesis can be entertained at all unless it meets 
in some measure the demand with reference to which it was 
invented, viz., a unification of conflicts in experience. And, 
in so far, it is confirmed. The motive which casts doubt 
upon its adequacy is the same that leads to its re-forming 
as a hypothesis, as a mental concept. 

The difficulties in Wundt's position are thus due to a 
failure to take account of the reconstructive nature of the 
judgment. The predicate, supposition, or hypothesis, what- 
ever we may choose to call it, is formed because of the check 
of a former habit. The judgment is an ideal application of 
a new habit, and its test is the attempt to act in accordance 
with this ideal reconstruction. It must not be thought, how- 
ever, that our supposition is first fully developed and then 
tried and accepted or rejected without modification. On 
the contrary, its growth is the result of successive minor 
tests and corresponding minor modifications in its form. 
Formation and test are merely convenient distinctions in a 
larger process in which forming, testing, and re-forming go 
on together. The activity of experimental verification is not 
only a testing, a confirming or weakening of the validity of 
a hypothesis, but it is equally well an evolution of the mean- 
ing of the hypothesis through bringing it into closer rela- 
tions with specific data not previously included in defining 
its import. Per contra, a purely reflective and deductive 
consideration which develops the idea as hypothesis, in 
so far as it introduces the determinateness of previously 
accepted facts within the scope, comprehension, or intension 
of the idea, is in so far forth, a verification. 

If the view which we have maintained is correct, the hypo- 
thesis is not to be limited to those elaborate formulations of 
the scientist which he seeks to confirm by crucial tests. The 



The Nature of Hypothesis 183 

hypothesis of the investigator differs from the comparatively- 
rough conjecture of the plain man only in its greater preci- 
sion. Indeed, as we have attempted to show, the hypothesis 
is not a method which we may employ or not as we choose; 
on the contrary, as predicate of the judgment it is present 
in a more or less explicit form if we judge at all. Whether 
the time and labor required for its confirmation or rejection 
is a matter of a lifetime or a moment, its nature remains the 
same. Its function is identical with that of the predicate. 
In short, the hypothesis is the predicate so brought to con- 
sciousness and defined that those features which are not 
noticed in the ordinary judgment are brought into promi- 
nence. We then recognize the hypothesis to be what in 
fact the predicate always is, viz., a method of organization 
and control. 



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